Just recently we had a topic by RodHull about his abitious project to trace letters from the Book of Kells. Let's see how all of you would go about drawing the trefoil knot in the manual's example.
If you are willing to experiment, try redrawing that over a solid grey background but without the black outlines.
Maybe add in some shading and a repeating pattern? -Let's not just rush that much. Step by step, knot's up!
I think of it as more of a conceptual challenge rather a fancy one. It would be advanced if all the fancy stuff is added in -like actual rope pattern along the knot, gradients etc.
There are a couple ways to draw this. (Had a series of solutions shared at openclipart. No sneek peek at the moment...)
My assumption is in the manual what we see as a knot is like one path and two clones rotated, all having a black stroke for the outlines.
It's more of like the previous vector art optimisation challenges we had with dozens of solutions producing the exact appearance.
So that we can share and develop a suitable drawing process.
To answer the question: it's for everyone -beginners most welcomed.
Ok, I made a version in the only way I know how (in 3 separate pieces) (I think it could be done with 2 pieces). But I found a little bit faster way.
I used to add new nodes in the necessary places. But it's too fidgety to add new nodes to intersections. So this time, I used Cut Path. The paths simply get cut in the right places already. Then I can node edit in a few places, and delete the rest.
I made just one loop, then duplicated and rotated. I made a version with squared off corners, instead of rounded.
Well, I'm not keen to re-draw it. But I'll put a gray background behind it, and remove the strokes. Is that to show the anti-alias issue, with the gray background?
Yes. Also a hint that the outline strokes alone can be drawn separate to the fill. And even better, if they are drawn as one object. Double strokes atop eachother can be avoided.
Something like in this attached svg for a start. Almost there.
Here is a sketch on the layout. The trefoil is constructed from three rings. From this point it is equally easy to turn this into interlocking rings or a trefoil knot.
After some duplicating and boolean operations, the "problematic" intersections are separated:
All is fine, except for the aforementioned gap issue.
Needs some overlapping.
But where? How?
One of those double path segments needs to be edited.
If they have the same fill colour as their neighboring path, they will appear uncut with proper overlapping.
Can be done many ways.
But which path should be at the top in the z-ordering, or wich of those should overlap?
One consideration would bee keeping an overall simple outline, with the shapes repeating in a symmetric layout -also where the object's z-order is in symmetric alignment.
That means for start, raising the repeating parts on the same level and then adding the same "joins".
Think of the paths as paper cut into the right shapes, then adding extra "limb" -space for a glue area.
From that perspective I'd prefer the topmost objects intact and the bottom ones having the "extra" space edits -so that one could glue them put on the table; and stack the smaller parts atop at the intersections.
(Like, this way the top paper doesn't need to be flipped to add the glue.)
Here are those principals in action:
-these are all svg-s, open them in inkscape to check-
With the right fill colours this still can be made into either interlocking rings or into a trefoil knot.
For finishing it up, adding the separate outlines drawn on top and some backdrop as in my previous post:
To sum it up, in this approach the fill was drawn with 15 paths in total and there was another one atop for the outlines.
Surely the number of paths used can be simplified much, yet the construction and structure will be less self-explanatory.
ok, I've wanted to do this for a long time - so throwing my hat in, here's my huge FAIL, lol. I thought instead of the oval shape, I'd try doing the sides. I tried all sorts of crazy things and I think I've gone insane trying! you'all have got to stop torturing this ole gal with this crazy stuff. anyway, I cheated and looked at a couple of you tube vids - to not avail. Ended up with nick's, but couldn't figure out how he joined his nodes and they remained in the overlap, my nodes would not join for some reason, very strange. anyway, here's my attempt, feel free to laugh, or better yet, tell me how to fix it.
Lazur. I need to follow a tut, too stupid for this! and now my eyes are crossed over trying. If you get a moment, would you'all mind trying nick's video and tell me why my nodes don't join like his. It's just not making common sense to me.
We have all been there, gaining experience. That is an important process.
Skipping through the video.
Daryl is drawing the whole shape as one compound path, and hiding the intentionally wide cuts with a thick stroke.
So far your image looks as if it was drawn as in the left part of the video -finished around at the 7:00 mark.
That is supposed to represent the inner intersections of those "3 rings" -arcs.
Then he continues to draw the "joins" of those arcs, separately. He finishes with that path at 9:00.
After that, he crops the "unnecessary" part off from the second path, to retain the clean joins and adds that to the previously drawn inner parts after perfect alignment.
One general problem with this method is: with the Boolean operation -Ctrl++- performed, the double, curved path segments atop each other will result in randomly added nodes in odd positions.
(For that matter converting stroke to path isn't an accurate construction step either.)
The cutting performed after 5:00 determines the outcome largely. Without that the paths would merge together leaving with the same shape as at 9:00.
However even if keeping most of this could work with some precaution and no outsetting.
Paths should be broken apart, added together to 3 separate paths (and maybe combining them at last if one path is preferred).
Lazur. I need to follow a tut, too stupid for this! and now my eyes are crossed over trying.
The gist of it is to draw similar paths to these (svg):
Then adding the paths marked with the same hue values together, then combining them and adding a stroke to it.
In reality he not exactly does this because he have those joins already as a compound path and by adding all together the previous cuts at the intersections would vanish so adds in a wide offsetting there.
-Attaching the result after a bit of a cleanup too.
ah, thx, it's at the 5:00 mark that I didn't get. I couldn't join the nodes, only could do a path union, which of course isn't right. I think I understand your concept better. will give that a try over the weekend. thanks!
In the last examples can you color each segment differently, and as shown in the manual?
Yes.
Left out colouring from the equation to concentrate on the structure.
One could draw a gradient crossing and along the knot too in all of these examples. Gradient along the knot being the harder challenge this case for more reasons.
Ok, here's an improvement, has some broken lines, a bit crooked etc, but since I've pulled out all my hair doing this, thought I'd show it anyway, ha ha ha. You'all are trying to kill me, I know this Lazur! I had attempted to document my steps, but then I ended up not knowing what I did, couldn't reproduce this if my life depended on it, so no documentation. I had to let go of that video and go with my own thoughts. Will be sure to keep LOTS of copies of it, that's for sure. ha! good challenge!
Ok, here's an improvement, has some broken lines, a bit crooked etc, but since I've pulled out all my hair doing this, thought I'd show it anyway, ha ha ha. You'all are trying to kill me, I know this Lazur! I had attempted to document my steps, but then I ended up not knowing what I did, couldn't reproduce this if my life depended on it, so no documentation. I had to let go of that video and go with my own thoughts. Will be sure to keep LOTS of copies of it, that's for sure. ha! good challenge!
Sorry for the frustration.
Maybe I'll look into jessyink and convert those example trefoils into bulletpoint animations to better show their structure/z-ordering of the objects.
Before compltely hijacking this topic though, started another one because I feel there is some potential in colouring such a knot.
For me, correctly interlacing / cutting paths in knots always seemed to be a magic trick... 'Till I found this method : https://www.youtube.com/watch?v=mf7m4m0Wtng (sorry, it's in french 😖).
In Inkscape, intersections (graph templates) are placed first, using a clone to fix and change globally the way paths cross each other. Each red line acts as a wall for the paths : they can cross them only at a junction ( = doors in the wall). To complete pattern, paths are added to join each intersection with it's nearest neighbour, without crossing walls.
Where do you find the graph template? Do you have to make it yourself?
I've done something similar, where I used the same intersection, and rotated it as needed for different crossover areas. But I didn't make a template. I just duplicated and rotated.
I can't find the exact image, but it was something like the crossovers in this one.
For me, correctly interlacing / cutting paths in knots always seemed to be a magic trick... 'Till I found this method : https://www.youtube.com/watch?v=mf7m4m0Wtng (sorry, it's in french ). In Inkscape, intersections (graph templates) are placed first, using a clone to fix and change globally the way paths cross each other. Each red line acts as a wall for the paths : they can cross them only at a junction ( = doors in the wall). To complete pattern, paths are added to join each intersection with it's nearest neighbour, without crossing walls. A try I made using it :
Glad you joined in!
That video is a great inspiration, for more "waffle attack" in the future.
Do you happen to know this album? It had two intricate knotworks as an album cover.
I tried to "retroengineer" the cover, that works pretty well :
Nice!
That method seems quite effective laying out new knot designs and you are very good with that!
Your previous waffle knot made me wonder if any random shape could be filled with a knot pattern. Well, if knitting is considered or crocheting then it's definitely possible while the knot is getting ridiculously complex as a "knot".
Got the idea to draw one shaped as a Christmas tree to stay in season.
@Lazur, in the tree shaped image, how did u create the perfect green background for a vector... i have some vectors where i need to create a background in the same shape as the original vector. Bezier tool takes a long time and does not look as clean as the tree you have posted. can you help explain how to go about it?
I tried a new approach to the celtic knot. I relied heavily on clones, so there is one "foil", on which I work and which has a clipping mask. This way, I can clone it twice and it blends seamlessly.
This makes it easy to change things, for example to have an "impossible" knot. (second example).
Drawing Challenges, Contests, Competitions Draw a knot challenge
Inkscape.org
It has always been a challenge to depict a knot. Thinking of how it is built up in 3D, it certainly does. Even the manual offers that as a challenge to draw, seen here: http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Challenges-Knot.html
Just recently we had a topic by RodHull about his abitious project to trace letters from the Book of Kells. Let's see how all of you would go about drawing the trefoil knot in the manual's example.
If you are willing to experiment, try redrawing that over a solid grey background but without the black outlines.
Maybe add in some shading and a repeating pattern? -Let's not just rush that much. Step by step, knot's up!
Is this for advanced users? I can only think of one way to do it. Or maybe you can clarify a little?
I think of it as more of a conceptual challenge rather a fancy one. It would be advanced if all the fancy stuff is added in -like actual rope pattern along the knot, gradients etc.
There are a couple ways to draw this. (Had a series of solutions shared at openclipart. No sneek peek at the moment...)
My assumption is in the manual what we see as a knot is like one path and two clones rotated, all having a black stroke for the outlines.
It's more of like the previous vector art optimisation challenges we had with dozens of solutions producing the exact appearance.
So that we can share and develop a suitable drawing process.
To answer the question: it's for everyone -beginners most welcomed.
Ok. I'll be interested to see the other ways.
Ok, I made a version in the only way I know how (in 3 separate pieces) (I think it could be done with 2 pieces). But I found a little bit faster way.
I used to add new nodes in the necessary places. But it's too fidgety to add new nodes to intersections. So this time, I used Cut Path. The paths simply get cut in the right places already. Then I can node edit in a few places, and delete the rest.
I made just one loop, then duplicated and rotated. I made a version with squared off corners, instead of rounded.
I see we still have 1 inch thumbnails....too bad.
Nice! That's what I thought was drawn in the manual -by the way there is an extra 4th path in your drawing.
*gap issue intensifies*
Well, I'm not keen to re-draw it. But I'll put a gray background behind it, and remove the strokes. Is that to show the anti-alias issue, with the gray background?
Let's see if it will show in a PNG.
(stupid tiny thumbnails 😠)
Yes. Also a hint that the outline strokes alone can be drawn separate to the fill.
And even better, if they are drawn as one object. Double strokes atop eachother can be avoided.
Something like in this attached svg for a start. Almost there.
Hmm thought it would gain more interest.
Attaching a few svg-s of the thought process.
Here is a sketch on the layout. The trefoil is constructed from three rings. From this point it is equally easy to turn this into interlocking rings or a trefoil knot.
After some duplicating and boolean operations, the "problematic" intersections are separated:
All is fine, except for the aforementioned gap issue.
Needs some overlapping.
But where? How?
One of those double path segments needs to be edited.
If they have the same fill colour as their neighboring path, they will appear uncut with proper overlapping.
Can be done many ways.
But which path should be at the top in the z-ordering, or wich of those should overlap?
One consideration would bee keeping an overall simple outline, with the shapes repeating in a symmetric layout -also where the object's z-order is in symmetric alignment.
That means for start, raising the repeating parts on the same level and then adding the same "joins".
Think of the paths as paper cut into the right shapes, then adding extra "limb" -space for a glue area.
From that perspective I'd prefer the topmost objects intact and the bottom ones having the "extra" space edits -so that one could glue them put on the table; and stack the smaller parts atop at the intersections.
(Like, this way the top paper doesn't need to be flipped to add the glue.)
Here are those principals in action:
-these are all svg-s, open them in inkscape to check-
With the right fill colours this still can be made into either interlocking rings or into a trefoil knot.
For finishing it up, adding the separate outlines drawn on top and some backdrop as in my previous post:
To sum it up, in this approach the fill was drawn with 15 paths in total and there was another one atop for the outlines.
Surely the number of paths used can be simplified much, yet the construction and structure will be less self-explanatory.
Here is a middle-ground with 6 paths:
Another solution, with only 3 paths used for the fil, one atop anotherl -each having a unique shape, despite the appearance.
Method can be applied here as well:
After uploading the image in the attachment, there is an option to embed it into the html -second icon on the right side of the spinbox thingy
ok, I've wanted to do this for a long time - so throwing my hat in, here's my huge FAIL, lol. I thought instead of the oval shape, I'd try doing the sides. I tried all sorts of crazy things and I think I've gone insane trying! you'all have got to stop torturing this ole gal with this crazy stuff. anyway, I cheated and looked at a couple of you tube vids - to not avail. Ended up with nick's, but couldn't figure out how he joined his nodes and they remained in the overlap, my nodes would not join for some reason, very strange. anyway, here's my attempt, feel free to laugh, or better yet, tell me how to fix it.
and here's nick's video - curious to see if anyone else gets a good output! https://www.youtube.com/watch?v=u6uHQo_EmQ0&t=197s
Lazur. I need to follow a tut, too stupid for this! and now my eyes are crossed over trying. If you get a moment, would you'all mind trying nick's video and tell me why my nodes don't join like his. It's just not making common sense to me.
Glad you give it a try!
We have all been there, gaining experience. That is an important process.
Skipping through the video.
Daryl is drawing the whole shape as one compound path, and hiding the intentionally wide cuts with a thick stroke.
So far your image looks as if it was drawn as in the left part of the video -finished around at the 7:00 mark.
That is supposed to represent the inner intersections of those
"3 rings"-arcs.Then he continues to draw the "joins" of those arcs, separately. He finishes with that path at 9:00.
After that, he crops the "unnecessary" part off from the second path, to retain the clean joins and adds that to the previously drawn inner parts after perfect alignment.
One general problem with this method is: with the Boolean operation -Ctrl++- performed, the double, curved path segments atop each other will result in randomly added nodes in odd positions.
(For that matter converting stroke to path isn't an accurate construction step either.)
The cutting performed after 5:00 determines the outcome largely. Without that the paths would merge together leaving with the same shape as at 9:00.
However even if keeping most of this could work with some precaution and no outsetting.
Paths should be broken apart, added together to 3 separate paths (and maybe combining them at last if one path is preferred).
The gist of it is to draw similar paths to these (svg):
Then adding the paths marked with the same hue values together, then combining them and adding a stroke to it.
In reality he not exactly does this because he have those joins already as a compound path and by adding all together the previous cuts at the intersections would vanish so adds in a wide offsetting there.
-Attaching the result after a bit of a cleanup too.
ah, thx, it's at the 5:00 mark that I didn't get. I couldn't join the nodes, only could do a path union, which of course isn't right. I think I understand your concept better. will give that a try over the weekend. thanks!
Some more variants.
6 paths on the fill, 2 of them being identical.
Next solution has the same layout, but cuts are positioned outside the joins.
This path arrangement can make it easy to be reproduced only with paths that have strokes set only and no fills.
Needless to say, that means a bit more complicated z-ordering. Like, instead of 2 layers of fill with an outline atop,
now it's a layer of stroke, a layer of "fill" above them, then another layer of strokes and another layer of "fills".
Pro: all widths can be adjusted in a later stage.
Con: the joins can't be set to be extrapolated -in the example rounded joins are used.
Check the svg-s for the details.
In the last examples can you color each segment differently, and as shown in the manual?
Yes.
Left out colouring from the equation to concentrate on the structure.
One could draw a gradient crossing and along the knot too in all of these examples. Gradient along the knot being the harder challenge this case for more reasons.
Ok, here's an improvement, has some broken lines, a bit crooked etc, but since I've pulled out all my hair doing this, thought I'd show it anyway, ha ha ha. You'all are trying to kill me, I know this Lazur! I had attempted to document my steps, but then I ended up not knowing what I did, couldn't reproduce this if my life depended on it, so no documentation. I had to let go of that video and go with my own thoughts. Will be sure to keep LOTS of copies of it, that's for sure. ha! good challenge!
What spinbox thingy?
The bar you can type in the name of the file.
Here is the button:
Oooohhh. Ok, thanks.
Sorry for the frustration.
Maybe I'll look into jessyink and convert those example trefoils into bulletpoint animations to better show their structure/z-ordering of the objects.
Before compltely hijacking this topic though, started another one because I feel there is some potential in colouring such a knot.
The first idea is here.
For me, correctly interlacing / cutting paths in knots always seemed to be a magic trick... 'Till I found this method :
https://www.youtube.com/watch?v=mf7m4m0Wtng (sorry, it's in french 😖).
In Inkscape, intersections (graph templates) are placed first, using a clone to fix and change globally the way paths cross each other.
Each red line acts as a wall for the paths : they can cross them only at a junction ( = doors in the wall).
To complete pattern, paths are added to join each intersection with it's nearest neighbour, without crossing walls.
A try I made using it :
HQ version available here :
https://www.deviantart.com/m-1981/art/Graph-knot-study-822843757
Where do you find the graph template? Do you have to make it yourself?
I've done something similar, where I used the same intersection, and rotated it as needed for different crossover areas. But I didn't make a template. I just duplicated and rotated.
I can't find the exact image, but it was something like the crossovers in this one.
M1981. fabulous! will have to look at the vid, too bad I don't remember much of my french lessons from 45 yrs ago, lol.
Brynn, that design is amazing, whomever did it. Wasn't sure if I understand that it is not yours.
Glad you joined in!
That video is a great inspiration, for more "waffle attack" in the future.
Do you happen to know this album? It had two intricate knotworks as an album cover.
Thanks Dee. I drew that for my coloring pages (hopefully someday, coloring book) project.
nevermind
Hi @Lazur , I didn't know this album, thanks for the discovery !
I tried to "retroengineer" the cover, that works pretty well :
https://www.deviantart.com/m-1981/art/Knot-retroengineering-824241377
The graph reminds me a turtle carapace - polynesians patterns are not so far...
Nice!
That method seems quite effective laying out new knot designs and you are very good with that!
Your previous waffle knot made me wonder if any random shape could be filled with a knot pattern. Well, if knitting is considered or crocheting then it's definitely possible while the knot is getting ridiculously complex as a "knot".
Got the idea to draw one shaped as a Christmas tree to stay in season.
Here it goes; Merry Christmas to all!
Oh, the weave part is awesome!
A couple of "branches" missed their overlap though. Maybe because the strands are just too close together?
Oh yeah, there would be no way to loop those through all the layers - not without moving some over a little bit.
Ok, took way more time than I'd care to admit, but here is some update on that tree-shaped one.
Not exactly that one, but these two animated ones:
animated knot 1
animated knot 2
Very nice animation!
Amazing!
Wow, the animated ones are fantastic. Now that's thinking outside the box!
That same knot has a crop circle. 2002 June 2nd.
Anyone up to the challenge, by all means feel free. Crop Circle Connector will gladly post your diagrams.
All skill levels are welcome to email art to Cropcircleconnector.com.
As far as I can tell, there are only about a dozen or so artists submitting diagrams.
The designs are free; Without copy-write. With inkscape we can .svg the world's largest mandalas!
Crop circles are world-wide. Examples of art we all share in our social memory.
Our combined efforts might even strengthen the velocity forward, toward a probability of open contact.
@Lazur, in the tree shaped image, how did u create the perfect green background for a vector... i have some vectors where i need to create a background in the same shape as the original vector. Bezier tool takes a long time and does not look as clean as the tree you have posted. can you help explain how to go about it?
Here is my trifoil celtic knot.
There are a few "broken" areas in the "pattern along path", but all in all, I am quite OK with the outcome.
I tried a new approach to the celtic knot. I relied heavily on clones, so there is one "foil", on which I work and which has a clipping mask. This way, I can clone it twice and it blends seamlessly.
This makes it easy to change things, for example to have an "impossible" knot. (second example).